One of the main causes of passenger pigeons going extinct was the loss of the eastern hardwood forests. Without large stretches of oak and beechnut for feeding and nesting the passenger pigeons had nowhere to live. Not that the hunting helped any.

Passenger pigeons were once probably the most numorous birds on the planet. There were about 5 billion of them in North America, and flocks could darken the sky for hours-- sometimes days. The flocks were so thickly packed that a single shot could bring down thirty or forty birds and many were killed simply by hitting them with pieces of wood as they flew over hilltops. Nesting flocks would cover from 30 to 850 square miles of forest, and have up to 100 nests in a single tree.

P.S. I have conflicting sources. I am inclined to believe David Quammen in his book Natural Acts when he claims that habitat loss was the main cause of the passenger pigeon's extinction. But http://www.eco-action.org/dt/pigeon.html favors the over hunting theory:

The population had certainly been reduced by the middle of the nineteenth century but was still several billion strong. The real onslaught began with the onset of large-scale commercial hunting carried out by well-organised trappers and shippers in order to supply the developing cities on the east coast of the United States with a cheap source of meat. It began once railways linking the Great Lakes area with New York opened in the early 1850s. By 1855 300,000 pigeons a year were being sent to New York alone. The worst of the mass slaughter took place in the 1800s and 1870s. The scale of the operation can be judged by figures that seem almost incredible but which were carefully recorded as part of a perfectly legal and highly profitable commerce. On just one day in 1860 (23 July) 235,200 birds were sent east from Grand Rapids in Michigan. During 1874 Oceana County in Michigan sent over 1,000,000 birds to the markets in the east and two years later was sending 400,000 a week at the height of the season and a total of 1,600,000 in the year. In 1869, Van Buren County, also in Michigan, sent 7,500,000 birds to the east. Even in 1880, when numbers had already been severely reduced, 527,000 birds were shipped east from Michigan.

Impressive statistics. I could be wrong. But I think the loss of hardwood forests may have been the only reason the hunting took such a toll. 7 million isn't even one percent of the original population of passenger pigeons. Even with this rate of deaths over an extended period of time, it doesn't account for the rapid disappearance of the passenger pigeons. (Without any new births, -20,000,000 million a year out of 3 billion will last 150 years. 1850 to 1914 is 64 years. It is possible the natural death rate overtook the birth rate, tho.)